Independent random variables on Abelian groups with independent the sum and difference

2015/10/16 by Gennadiy Feldman, Feldman, G. M. · 1 citation
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Functional Equations Stability Results #Probability (math.PR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1510.04798

openalex publication_date 2015/10/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let X be a second countable locally compact Abelian group. Let ξ₁, ξ₂ be independent random variables with values in the group X and distributions μ₁, μ₂ such that the sum ξ₁+ξ₂ and the difference ξ₁-ξ₂ are independent. Assuming that the connected component of zero of the group X contains a finite number elements of order 2 we describe the possible distributions μ_k.

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